Hello everyone, I am kind of a beginner with arduino, I tried to search the web and the forum before posting this topic. Please forgive me if it is stupid:

I have a 9V AC source, I will use a rectifier (or 4 diodes I am not sure yet) and a capacitor to convert it to DC, can connect the Vin pin of my Arduino UNO to it to power the arduino? or should I use a regulator?

Yes, this should work. You are essentially constructing a DC wall transformer by taking an AC source and rectifying it.

Depending on how much current you will be drawing from this power supply, your voltage may drop below the 6.5V or so needed for proper regulation. Sizing your DC capacitor will become important, as is the characteristics of the 9VAC source itself of course.

Thanks for the quick reply. That was also my first thought, but wanted a more experienced opinion.

Now a trickier question :

I know that the capacitor will influence the AC source, would that be problematic in case I need the original 9vAC to remain intact? (I need the wave form to remain a nice sine and the voltage to be as authentic as possible, it is to measure the wall socket RMS).

Well, you're going to be in for a surprise if you think you're going to see a nice sine wave to begin with

Any load you place on your AC transformer (i.e., current draw) is going to distort the signal, either in shape or in amplitude, unless you have a "perfect" AC transformer (don't bother looking for one). The bigger (higher power) the transformer the less you will distort the wave.

As with all engineering problems, it depends How much accuracy do you need? What load currents (beyond the Arduino) will you be pulling from the supply? etc. etc.

Maybe it's easiest to just try it. Look at the voltage waveform on the AC side (carefully...don't do it if you don't know what you're doing and what an 'earth-grounded oscilloscope' is, or maybe you have an isolated voltage probe), then look at it on the transformer side and see if the waveshape is preserved by your transformer. Then hook up your bridge rectifier and capacitor and a dummy load (100 ohm 2W power resistor might be a good load) and see how it changes. Too much? Then go to plan B.....

Of course, "looking" at waveforms is not a measure of quality (looking at total harmonic distortion on a spectral plot is better) but at least it's a start.